Suppose a E R, where a > 0, a ± 1, what is[a*]? d @ xa²-1 xa"-1. In(a) © a² a* In(a)

Q: Evaluate the definite integral S (1+ 2x) dx using Riemann sum.

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Q: 5₂00⁰ dx 2 3 1.

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Q: 1. Write the improper integral which is represented by the following limit. lim C2" 2x dx x2-4 2.…

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Q: 6. The improper integral dx converges to /x- 5 '5 Vr-5

A: The given integral is an improper integral of second kind.

Q: Determine maximum error between 0 ≤ ? ≤ ?/3 interval for fourth degree Taylor expansion of ?(?) =…

A: Determine maximum error between 0 ≤ ? ≤ ?/3 interval for fourth degree Taylor expansion of ?(?) =…

Q: Determine if the improper integral el/x dx x2 converges or diverges. If it converges, find its…

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Q: Find where ln((1+z)/(1-z)) is not analytic.

A: To find: The region where the function ln(1+z)(1-z)), where z∈ℂ is not Analytic.

Q: The area above the x-axis, below the graph of f(x) = between x=0 and x=2 is the limit of 1+z which…

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Q: If the integral diverges, indicate that using the checkbox. 6 dx The integral diverges x(x + 1)

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Q: 8. Use Simpsons' rule to numerically integrate for the n = 6, case f (x) = x on the unit interval,…

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Q: se limit is a "dx" integral

A: Given as,

Q: Show that e grows faster as x –→∞ than x" for any positive inte- ger n, even x'-000,000. (Hint: What…

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Q: Use a second Taylor polynomial at x = 0 to estimate the areaunder the curve y = ln(1 + x^2) from x =…

A: Given that, y=ln1+x2 To estimate the area under the curve from x=0 to x=12, use the second Taylor…

Q: O Use a linear approxi mation (differential) to estimate 3999

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Q: Use trapezoidal with 3 level romberg (k=3) to evaluate the integral from lower limit 0 to upper…

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Q: Suppose that f is an integrable function on R (real numbers).  How do you show that the integral  of…

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Q: ∞ e4y dy

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Q: Evaluate the indefinite integral as an infinite series. / arctan (a") de

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Q: Only one of these calculations is correct to evaluate the definite integral Inx dx Select one: 1 Inx…

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Q: Prove that integration of (x/sigma square ) times exponential of (-x square/2sigma square) for limit…

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Q: Evaluate the integral if it converges. Enter the exact answer, or enter na if it diverges. +00 -dx =…

A: Let I is the value of given Integral.

Q: 4 A function fx) = 1- x² + xr is defined in the closed interval [-1, 1]. The value of x in i onen…

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Q: 6 Jlgul sin (nx +3) 1,(x) =- is convergent point wise to zero function. n-1 ylgn O Ihi O

A: Calculate limn→∞fn:  limn→∞fn=limn→∞sinnx+3n-1             =0

Q: Evaluate the indefinite integral as an infinite series. 1 13. COS X dx x2

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Q: The integral of ƒ In(ln(x))dx can not be expressed as a finite sum of functions. What do we call…

A: It is called as non elementary integral

Q: Evaluate the indefinite integral as an infinite series. ex- 1 dx 2x + C n = 1

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Q: 8. Use Simpsons' rule to numerically integrate for the n = 6, case f(x) = x on the unit interval,…

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Q: Show if x, is convergent or divergent T.3 'n sin(x) dx 1+x S'

A: Introduction: The convergence or divergence of an infinite series depends upon the sum of the…

Q: Explain why the improper integral (x + 3) sin(x) dx L. (x² + 1)(x² + 4)² is convergent. 8

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Q: | de P8- メレー Oe dedx

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Q: /tangent slupe rosin (20) when dy ス 5. 555 653 3. not of thc above

A: Topic:- application of derivatives in polar form

Q: What is the area beneath the curve y=x2 +1 and above the x-axis from x = 0 to x = 4 by using the…

A: Here we have to use Riemann right end sum

Q: An odd piecewise continuous function f(x) on every finite interval of (-0, 0) such that / fx)| dxis…

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Q: sin x dx S1 2C

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Q: f(x) = | tan-1(x9) dx f(x) = C + > n = 0

A: The Power series expansion of  tan-1x=x-x33+x55-x77+... Therefore, the power series expansion of…

Q: .5 Estimate the middle Riemann sum for 1 dx (n= 4). 3 1-lnx

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Q: Evaluate the indefinite integral as a power series. tan dt

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Q: 1. Use the definition of the definite integral as the limit of a sum to evaluate (4.x – 2²) dx.

A: The given problem can be solved as-

Q: Evaluate the indefinite integral as an infinite series. | arctan(x2) dx Σ + C n = 0

A: Answer

Q: x° sin(x³) In(4 + cos(x³)) if x 10° ya. 00 Determine whether or not the improper integral dx…

A: We have to use comparison test here.

Q: An even piecewise continuous function f(x) on every finite interval of (-oo, 0) such that :/ (x)|…

A: The given statement is : An even piecewise continuous function f(x) on every finite interval of -∞,∞…

Q: x4 In(1 + x) dx Σ 00 f(x) = C + n = 0

A: The given integral is  ∫x4ln1+xdx

Q: 55. Show that dx J+4 converges by comparing with x³ + xdx. -3 dx. х

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Q: 1. Approximate |(x² +e*) dx using a Riemann Sum with n=6 and right endpoints. Round result to the…

A: We have ∫06x2+exdx with n=6

Q: Evaluate the indefinite integral as a power series. integral of (tan^−1(x)/x)dx. What is the radius…

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Q: Evaluate the indefinite integral as an infinite series. arctan(x5) dx Σ( |)•c n = 0

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Q: (a) (6) Decide if the following improper integrals are convergent or divergent using Basic…

A: To decide the convergence of the improper integrals.

Q: b) Determine whether the improper integral `1+ sin r -dx 1+x² converges or diverges.

A: Comparison test :  Suppose for x>a  . If converges then also converges . If diverges then…

Q: Evaluate the definite integral S (1 + 2x) dx using Riemann sum.

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Q: Find Lebesque integral of function on segment (0,1) f(x) = if- 7h+1

A: In the given question we have to find the Lebesque integral of the given function…